Due to the excessive costs of oil well exploration, it is of utmost importance to know if a particular formation penetrated by a wellbore contains producible hydrocarbons. As will be appreciated by those skilled in the art, hydrocarbon saturation of a formation may readily be determined from the water saturation of the formation. Saturation as used herein is defined as the total fluid content of the formation, and water saturation, hereinafter referred to as S.sub.w, is that percentage of the total fluid content which is water. It will also be recognized by those skilled in the art, that hydrocarbon saturation, or S.sub.HY, is equal to 1-S.sub.w. Thus, it can be seen that once S.sub.w has been determined, S.sub.HY is readily obtainable.
There are at present many log evaluation and interpretation techniques for determining water saturation. These interpretation techniques are based on empirical relationships dependent upon a knowledge of porosity, .phi., resistivity of clean formations (R.sub.t) and resistivity of connate water (R.sub.w). For example, two well-known empirical relationships are employed. The relationship EQU F=a/.phi.m (1)
relates porosity (.phi.) to the formation factor (F), and the relationship EQU S.sub.w.sup.n =(F R.sub.w /R.sub.t) (2)
relates the formation factor (F) and resistivities (R.sub.w and R.sub.t) to the water saturation (S.sub.w). The formation factor, F, is known to vary with the resistivity of a clean formation and with the resistivity of a brine formation which is fully saturated and .phi., the porosity, is the fraction of the total volume of subsurface material occupied by pores or voids. The cementation factor "m", saturation exponent "n" and the coefficient "a" will be discussed hereinafter.
The parameters R.sub.t and porosity, .phi., may be determined directly from well-logging measurements. For example, R.sub.t is obtained from such well-logging operations as induction logging, and .phi. is obtained from such operations as borehole compensated sonic logs, formation density compensated logs, and other compensation porosity logs or combinations of these logs. A discussion of these different logs is available in "Log Interpretation Principles", published by Schlumberger Limited, 277 Park Avenue, New York, N.Y. (1972). R.sub.w (water resistivity) on the other hand, must be determined by empirical relationships from various direct logging measurements. Typical relationships include those discussed in a publication entitled "Log Analysis of Sand-Shale sequences--A systematic Approach;" by Poupon et al, published in the July 1970 issue of the Journal of Petroleum Technology.
In practice, the values of "a" (formation factor coefficient) and "m" (cementation factor) in equation 1, and "n" (saturation exponent) in equation 2, vary with the type of formation and heretofore have been applied as fixed values which were determined empirically for various lithology types. A correct choice of the proper value of these parameters is often difficult, especially in complex lithologies. Therefore, since the accuracy of S.sub.w is dependent upon these parameters, it is highly desirable to develop a new relationship for more accurately determining these parameters in all formations.
Several different equations and techniques are also presently used for determining permeability, K, of a formation from well-logging data. However, none of these techniques is universally applicable from field-to-field, well-to-well, or even zone-to-zone within a well, without making adjustments to constants or exponents, or other compensations. There are two relationships which are most often utilized for determining permeability, one is ##EQU1## This equation is based on empirical studies which found the permeability of certain formations to be relatable to the ratio of .phi. to S.sub.wirr through the use of a coefficient "C" and the exponents m and n. The coefficient "C" was generally found to be related to hydrocarbon type while the exponents m and n were found to apply to the type of lithology.
Another equation: ##EQU2## is a modified form of an equation developed by A. Timur (see "An Investigation Of Permeability, Porosity And Residual Water Saturation Relationships For Sandstone Reservoirs" by A. Timur, the log analyst, Volume 9, No. 4, July-August, 1968) which is simply an adaptation of equation 3 for the specific condition of a relatively clean, consolidated sandstone formation of medium porosity. Since "m" and "n" are lithology dependent, any attempt to fix them at constant values automatically induces errors when applied in non-standard conditions. This is particularly apparent when these relationships are used for fine-grained or shaly formations. Such applications demonstrate the need for developing a more accurate technique for obtaining the permeability of a formation.
In accordance with this invention, relationships between the parameters for determining both water saturation and permeability are established and used to obtain more accurate representations of each of these formation parameters.